define Cox-Ingersoll-Ross interest rate model - Maple Help

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Finance[CoxIngersollRossModel] - define Cox-Ingersoll-Ross interest rate model

Calling Sequence

CoxIngersollRossModel(r, theta, kappa, sigma, x0)

Parameters

r

-

initial term structure

theta

-

long term mean level

kappa

-

speed of reversion

sigma

-

volatility

x0

-

initial value

Description

• 

The CoxIngersollRossModel command creates a Cox-Ingersoll-Ross model with the specified parameters. Under this model the short rate process rt has the following dynamics with respect to the risk-neutral measure

drt=κθrtdt+σrtdWt

where θ, κ, σ, and x0 are non-negative constants and W(t) is a Wiener process modeling the random market risk factor.

It is reasonable to require that σ2<2κθ.

Examples

withFinance&colon;

First define a Cox-Ingersoll-Ross model with parameters r0&equals;0.03, θ=0.05, κ=0.5, σ=0.002, and x0&equals;0.1.

M:=CoxIngersollRossModelZeroCurve0.03&comma;0.05&comma;0.5&comma;0.002&comma;0.1

M:=moduleend module

(1)

Here is the corresponding short rate tree.

T:=ShortRateTreeM&comma;5&comma;40

T:=moduleend module

(2)

TreePlotT&comma;axes&equals;BOXED&comma;thickness&equals;2&comma;gridlines&equals;true

See Also

Finance[BlackScholesProcess], Finance[HullWhiteModel], Finance[OrnsteinUhlenbeckProcess], Finance[PathGenerator], Finance[SamplePath], Finance[ShortRateProcess], Finance[ShortRateTree]

References

  

Brigo, D., Mercurio, F., Interest Rate Models: Theory and Practice. New York: Springer-Verlag, 2001.

  

Glasserman, P., Monte Carlo Methods in Financial Engineering. New York: Springer-Verlag, 2004.

  

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.


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